High vacuum in enormous volumes maybe. Otherwise it was certainly a problem solved decades ago.

Not sure what role of EUV optics was in LHC. But Zeiss would develop you anything on the frontier of optics if you have deep enough pockets.

The rest I don't know enough to comment on, but as far as technology goes both LHC and EUV lithography are bespoke systems. Seriously doubt there is any path dependency. Huge part of LHC cost were earthworks and precision construction of complex machinery at enormous scale.

EUV uses mirrors rather than lenses, and the precision surfaces on those are something that more likely came out of space programs. But honestly, I have no problem with throwing a few billion at basic science that might go nowhere. It's a drop in the ocean compared to war and corporate welfare.